1. Field of the Invention
The present invention is related to the field of well log interpretation. More specifically, the present invention is related to methods for determining porosity of earth formations using acoustic velocity well logging measurements, when the earth formations contain gas in the pore space.
2. Description of the Related Art
Well logging determining acoustic velocity of earth formations is known in the art. Well logging for determining acoustic velocity includes inserting a sonde, having acoustic transducers disposed thereon at axially spaced apart locations, into a wellbore penetrating the earth formations. One of the transducers, called a transmitter, periodically emits pulses of acoustic energy into the wellbore. The acoustic energy pulses interact with the wall of the wellbore so as to travel along the wellbore wall. Some of the energy eventually returns to other transducers, called receivers. The receivers generate electrical signals in response to the acoustic energy. Various electrical circuits, which can be disposed in the sonde or at the earth's surface, interpret the electrical signals to determine the amount of time taken by the acoustic energy pulses in traversing the distance between the transmitter and the receivers, or alternatively, between any two of the receivers. The amount of time the acoustic pulses take to traverse the distance can correspond to the acoustic velocity of the earth formations within which the sonde is positioned at the time the acoustic energy pulses are emitted and detected.
A typical acoustic well logging instrument can include different types of transmitters, and corresponding receivers, each type of transmitter emitting acoustic energy which propagates in a different mode. One type of transmitter can emit acoustic energy pulses that propagate in a mode in which the pulses travel through the earth formations at the compressional velocity of the earth formations. If the shear velocity of the earth formations is greater than the compressional velocity of the fluid filling the wellbore, this type of transmitter can also cause generation of shear energy by mode conversion at the wellbore wall, and this shear energy may be detected by the receivers. Another type of transmitter can emit acoustic energy pulses that propagate in a mode in which the pulses travel through the earth formations at a velocity which substantially corresponds to the shear velocity of the earth formations. The typical acoustic well logging tool can simultaneously generate travel time measurements corresponding to either or both the compressional and the shear velocities of the earth formations. A tool having an arrangement of transmitters and corresponding receivers capable of measuring both compressional and shear velocities is known in the art and is described, for example, in "Multipole Array Acoustilog", Western Atlas Logging Services, Houston, Tex., 1992.
As is understood by those skilled in the art, the compressional velocity of a particular earth formation can be related to the fractional amount of pore space present in the particular earth formation. The fractional amount of pore space, referred to as porosity, is a highly useful quantity and is determined, among other reasons, in order to estimate volumes of producible fluid which may be extracted from the particular earth formation. The porosity (referred to by the symbol .phi.) is typically determined from the compressional velocity by a relationship known in the an as the Wyllie time average relationship, which can be expressed as: ##EQU1## where .DELTA.t.sub.ma represents the compressional velocity (expressed in equation (1) as reciprocal velocity, or "interval travel time", usually presented in units of microseconds per foot) of the rock minerals making up the particular earth formation, .DELTA.t.sub.ft represents the interval travel time of fluid present in the pore space of the earth formation, and .DELTA.t.sub.log represents the interval travel time of compressional acoustic energy as measured by the acoustic well logging instrument.
As can be inferred from equation (1), the compressional velocities of the rock minerals and of the fluid in the pore space of the particular earth formation must be determined in order to calculate the porosity using the relationship in equation (1). Rock minerals of typical earth formations penetrated by wellbores for the purpose of extracting fluids typically consist essentially of combinations of quartz sand, limestone (calcium carbonate), and dolomite (calcium-magnesium carbonate), whose interval travel times are well known. For purposes of calculating the porosity of the earth formations from velocity measurements made by the acoustic logging instrument, the pore space is typically assumed to be filled with water. Water typically has an interval travel time within a range of 189 to 210 microseconds per foot.
As is understood by those skilled in the an, the pore space of some earth formations can contain gas. Gas typically has a substantially slower velocity (and therefore larger interval travel time) than does water or any other liquids which can be present in the pore space, such as crude oil. In a particular earth formation, the presence of gas in the pore space generally results in the particular earth formation having a slower compressional velocity (larger interval travel time) than if the same earth formation had pore space filled entirely with liquid. The porosity calculated from the compressional velocity (or interval travel time) using the relationship of equation (1) will therefore typically be erroneously high when gas is present in the pore space of the particular earth formation.
As is also known by those skilled in the art, measurements of shear velocity of earth formations are much less affected by the velocity of the material filling the pore space than are measurements of compressional velocity. Measurements of shear velocity are therefore relatively unaffected by the presence of gas in the pore space of the earth formations. A comparison of the compressional velocity with respect to the shear velocity which indicates a much larger effect on the compressional velocity than on the shear velocity can be indicative of hydrocarbons, particularly gas, being present in the pore space of the earth formation.
A method for indicating the presence of hydrocarbons, particularly gas, in the pore space of the earth formations from comparison of shear and compressional velocities is described, for example, in "The Acoustic Log Hydrocarbon Indicator", D. Michael Williams, Transactions of the SPWLA 31st Annual Logging Symposium, 1990. A limitation of the method described in the Williams reference is that the method does not include any provision for determining the correct value of porosity from the compressional velocity when the earth formations contain gas in the pore space.
Accordingly, it is an object of the present invention to provide a method of determining porosity of earth formation from compressional acoustic velocity of the earth formations which can be compensated for the effects of gas or light crude oil in the pore space of the earth formations.